I am using delta parameterization with WLSMV and categorical indicators to try to establish partial measurement invariance of a CFA model. My grouping item is 7 categories. Modification indices suggested that I free the a factor loading in group 1. Thus, in the group-specific model command, I specified the factor loading and thresholds to be freely estimated, and I fixed the scale factor at 1 in this group.

I am receiving an error stating that I have a singular matrix and that my model is not identified, referring me to parameter 256. Parameter 256 is a scale factor in group 7, referring to the same item that I fixed to 1 in group 1.

I am wondering if this error has to do with the fact that all scale factors are already fixed to 1 in group 1. Do I need to fix this scale factor to 1 in group 7 to compensate for the fact that it was already fixed in group 1?